DEM visualisation techniques: Sky-view factor

There are usually at least two ways of looking at something. You can say that shaded relief allows you to modify illumination direction to enhance the visibility of certain relief features. You can also say that shaded relief requires you to modify illumination direction. It would be nice to have a visualisation that shows a lot of topographic detail but does not require repeated experimentation with illumination directions.

Shaded relief is based on modelling directional illumination. What about diffuse illumination? Imagine standing under an overcast sky, without direct sunlight. You’re looking an an object with relief detail (let’s say a marble statue or the rough plaster on a building’s facade). Even though there is no directional illumination, you can see three-dimensional details on the surface. The reason is that the more exposed points on the surface receive more diffuse light (and therefore appear brighter) than the deeper points. (Well, yes, the deeper points also collect more dirt, so please imagine a clean statue or wall.)

In computer graphics, such diffuse illumination is known as ambient occlusion. Under the term openness, it has been presented by Yokoyama et al. (2002) as a DEM visualisation technique.

A more commonly used DEM visualisation technique based on diffuse illumination is sky-view factor (Zakšek et al., 2011). Like ambient occlusion and openness, sky-view factor visualisation is based on modelling diffuse illumination. The difference is that while openness assumes homogeneous illumination from all directions, sky-view factor assumes homogeneous illumination from all directions above, i.e. it models illumination of each point of a DEM by an evenly bright hemisphere centered on that point.

Pixel brightness changes result from the occlusion of parts of the “sky” by the surrounding topography. To reduce processing time, only the topography within a certain radius of the pixel in question is taken into account. Furthermore, it was found that it is not necessary to look at all DEM points within that radius but that the occlusion due to the surrounding topography can be estimated by looking at DEM elevations along a limited number (usually 16 to 36) of radial lines.

The resulting digital map of sky-view factor values contains a theoretical range of values from close to 0 (almost no light received by a DEM pixel) to 1 (maximum possible amount of light received by a pixel because no part of the “sky” is occluded). Except for deep, narrow holes, the portion of the “sky” that is occluded by the surrounding topography is usually small. Therefore, most pixels will usually have sky-view factor values between 0.7 and 1.0.

To be able to display the sky-view factor map as an image, this range of values will have to be converted into greyscale values. Depending on the actual range of sky-view factor values, this conversion can be adapted (histogram stretch).

Shaded relief image (illumination azimuth 315°, elevation 60°, 3x vertical exaggeration).

Shaded relief image (illumination azimuth 315°, elevation 60°, no vertical exaggeration). LIDAR data (c) LGL/LAD.

Sky-view factor image of the same area (histogram stretch 0.7-1.0).

Sky-view factor image of the same area (histogram stretch 0.7-1.0). LIDAR data (c) LGL/LAD.

As can be expected from the description of the algorithm, sky-view factor is particularly well suited for the visualisation of topographic depressions such as mining traces or hollow ways. Shallow topographic features in nearly horizontal parts of a DEM are not well visible in sky-view factor visualisation, because changes in “sky” occlusion will be very small. Of course, applying a stronger histogram stretch will enhance contrast, but the resulting images will appear increasingly noisy.

Shaded relief image (illumination azimuth 315°, elevation 60°, 3x vertical exaggeration) showing medieval mining traces. LIDAR data (c) LGL/LAD.

Shaded relief image (illumination azimuth 315°, elevation 60°, 3x vertical exaggeration) showing medieval mining traces. LIDAR data (c) LGL/LAD.

Sky-view factor image of the same area (histogram stretch 0.7-1.0).

Sky-view factor image of the same area (histogram stretch 0.7-1.0). LIDAR data (c) LGL/LAD.

References

Kokalj, Z., Zakšek, K., Oštir, K., 2011. Application of sky-view factor for the visualisation of historic landscape features in lidar-derived relief models. Antiquity 85(327), 263–273. [article link]

Yokoyama, R. Shlrasawa, M., Pike, R.J., 2002. Visualizing topography by openness: a new application of image processing to digital elevation models. Photogrammetric Engineering & Remote Sensing 68(3), 257–265. [article link]

Zakšek, K., Oštir, K., Kokalj, Z., 2011. Sky-View Factor as a relief visualisation technique. Remote Sensing 3, 398–415. [article link]

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2 thoughts on “DEM visualisation techniques: Sky-view factor

  1. Pingback: 200 years of grafitti in a rock shelter in Saxony, Germany | x years Before Present

  2. Pingback: DEM visualisation techniques: Openness | 2 and 3 Dimensions

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